Simulating orbits using laws of physics [closed]

Question

Over the past couple of weeks I've been trying to simulate orbits in a solar system simulation I am making as part of a University module. To cut things short, my simulation is written in C++ using the Ogre3D rendering engine. I have attempted to implement orbits using Newton's law of universal gravitation which made my planet head towards the sun in a straight line, pass through the sun and then come back to its starting position. I also tried the steps from 'Position as a function of time' section of this wikipedia article, but that did not work for me either.

I am driving the simulation with a simple Euler integration method. If anyone has any experience with this kind of simulation, or just generally knows a lot about these physics laws then any help or pointing me in the right direction would be greatly appreciated.

Answer 1

Consult the project "Moving stars around", there is an old C and a modernized Ruby version. (And now a C++ version?)

Short advice: Eulers methods are bad for energy conservation. explicit Euler increases energy, implicit Euler reduces energy. Just check it on the phase space picture of the harmonic oscillator y''+y=0.

Use symplectic integrators, the most simple and famous is the Leapfrog or Verlet method that already Newton used to reason about planetary movement.